Free Acceleration Calculator
Calculate acceleration with the formula a = (v − u) / t. Enter the initial velocity, the final velocity, and the time over which the change happens to get the acceleration in metres per second squared (m/s²) instantly.
Enter the initial velocity, final velocity, and time to find acceleration from a = (v − u) / t.
a = (v − u) / t. A negative value means deceleration (slowing down). Uses SI units: velocities in m/s, time in seconds, acceleration in m/s². Convert km/h to m/s by multiplying by 1000/3600 (≈ 0.2778).
Quick answer
Acceleration is the rate of change of velocity, calculated with a = (v − u) / t, where u is the initial velocity, v is the final velocity, and t is the time taken. The result is in metres per second squared (m/s²). For example, a car speeding up from 0 to 27 m/s in 9 seconds has a = (27 − 0) / 9 = 3 m/s², meaning its speed increases by 3 m/s every second.
Formula & method
a = (v − u) / t
- a — Acceleration (metres per second squared, m/s²)
- v — Final velocity (metres per second, m/s)
- u — Initial velocity (metres per second, m/s)
- t — Time taken for the change in velocity (seconds, s)
Average acceleration in metres per second squared (m/s²). Subtract the initial velocity from the final velocity, then divide by the time taken. A negative result means deceleration (the object is slowing down). The time t must be greater than zero, since dividing by zero is undefined.
v = u + a·t • u = v − a·t • t = (v − u) / a
Rearrangements of the same equation. Use v = u + a·t to find the final velocity after accelerating for a time t, or t = (v − u) / a to find how long a given acceleration takes to reach a target speed.
Examples
- Input
- u = 0 m/s, v = 27 m/s, t = 9 s
- Result
- a = 3 m/s²
- Why
- Apply a = (v − u) / t = (27 − 0) / 9 = 27 / 9 = 3 m/s². Starting from rest, the object gains 3 m/s of speed each second, reaching 27 m/s (about 97 km/h) after 9 seconds.
- Input
- u = 0 m/s, v = 27.778 m/s (100 km/h), t = 5 s
- Result
- a ≈ 5.5556 m/s²
- Why
- First convert the final speed: 100 km/h = 100 × 1000 / 3600 = 27.778 m/s. Then a = (27.778 − 0) / 5 = 5.5556 m/s². This is the average acceleration of a quick hatchback during a 0–100 km/h sprint.
- Input
- u = 30 m/s, v = 0 m/s, t = 6 s
- Result
- a = −5 m/s²
- Why
- Apply a = (v − u) / t = (0 − 30) / 6 = −30 / 6 = −5 m/s². The negative sign shows deceleration: the car loses 5 m/s of speed every second until it stops after 6 seconds.
- Input
- u = 0 m/s, v = 19.6 m/s, t = 2 s
- Result
- a = 9.8 m/s²
- Why
- Apply a = (v − u) / t = (19.6 − 0) / 2 = 9.8 m/s². A dropped object reaching 19.6 m/s after 2 seconds confirms the acceleration due to gravity, g ≈ 9.8 m/s², when air resistance is ignored.
- Input
- u = 2 m/s, v = 10 m/s, t = 4 s
- Result
- a = 2 m/s²
- Why
- Apply a = (v − u) / t = (10 − 2) / 4 = 8 / 4 = 2 m/s². The runner is already moving at 2 m/s, then accelerates to 10 m/s over 4 seconds, gaining 2 m/s of speed each second.
When to use this tool
- Finding the average acceleration of a vehicle, runner, or object from a known change in velocity over a measured time.
- Solving introductory physics or mechanics homework that uses the kinematic equation a = (v − u) / t.
- Checking a 0-to-60 mph or 0-to-100 km/h acceleration figure by converting the speed to m/s and dividing by the time.
- Estimating braking or deceleration when an object slows from a known speed to a stop (or to a lower speed) over a given time.
- Verifying the acceleration due to gravity in a free-fall experiment, where a dropped object should accelerate at about 9.8 m/s².
Common mistakes
- Confusing velocity with acceleration. Velocity (m/s) is how fast something moves; acceleration (m/s²) is how fast that velocity changes. A car cruising at a steady 30 m/s has high velocity but zero acceleration, because its speed is not changing.
- Forgetting the sign. When the final velocity is less than the initial velocity, the acceleration is negative — this is deceleration (slowing down). Dropping the minus sign turns a braking problem into an impossible speeding-up answer.
- Mixing units before calculating. The result is in m/s² only when velocities are in m/s and time is in seconds. Convert km/h to m/s by multiplying by 1000/3600 (≈ 0.2778), and convert minutes or hours to seconds first.
- Dividing by zero time. a = (v − u) / t is undefined when t = 0, because no change in velocity can occur in zero time. Always use a real, positive time interval.
- Reversing initial and final velocity. The formula is (final − initial), i.e. (v − u). Swapping them flips the sign of the answer and reports acceleration as deceleration or vice versa.
Frequently asked questions
What is the formula for acceleration?
The formula for average acceleration is a = (v − u) / t, where u is the initial velocity, v is the final velocity, and t is the time over which the velocity changes. Subtract the starting speed from the ending speed and divide by the time. The result is in metres per second squared (m/s²). For example, going from 0 to 27 m/s in 9 seconds gives a = (27 − 0) / 9 = 3 m/s².
What are the units of acceleration?
The SI unit of acceleration is the metre per second squared, written m/s² (or m·s⁻²). It means the velocity changes by a certain number of metres per second every second. An acceleration of 3 m/s² means the speed increases by 3 m/s each second. Other units you may see include km/h per second and the standard gravity g, where 1 g ≈ 9.80665 m/s².
What does negative acceleration mean?
Negative acceleration means the object is slowing down in the direction of motion — commonly called deceleration. It happens when the final velocity is smaller than the initial velocity, so (v − u) is negative. For example, a car braking from 30 m/s to 0 in 6 seconds has a = (0 − 30) / 6 = −5 m/s². The minus sign indicates the velocity is decreasing, not that the car is moving backwards.
How do I convert km/h to m/s for this calculator?
Multiply the speed in km/h by 1000 (metres in a kilometre) and divide by 3600 (seconds in an hour), which is the same as multiplying by about 0.2778. For example, 100 km/h = 100 × 1000 / 3600 = 27.78 m/s. Enter velocities in m/s so the acceleration comes out in m/s². To go the other way, multiply m/s by 3.6 to get km/h.
Is this average acceleration or instantaneous acceleration?
This calculator gives average acceleration — the total change in velocity divided by the total time, assuming the acceleration is constant over that interval. Instantaneous acceleration is the acceleration at a single moment and equals the slope of the velocity-time graph at that point. For uniformly accelerated motion (constant a), the average and instantaneous values are the same.
Why can't the time be zero?
Because acceleration is a change in velocity divided by time, a = (v − u) / t, and division by zero is mathematically undefined. Physically, no velocity change can occur in zero time, so the question has no meaningful answer. Always use a positive time interval; if you only have the distance instead of the time, use a kinematic equation such as v² = u² + 2·a·s instead.
Sources & references
- Acceleration - Wikipedia
- Acceleration - HyperPhysics (Georgia State University)
- Standard acceleration of gravity - NIST
External references open in a new tab. We are independent and not affiliated with these organizations.
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